In scientific notation, if a distance is expressed as 3.4 times 10 to the negative 6th centimeters, how many micrometers is this?

To convert the distance from centimeters to micrometers, it's essential to understand the relationship between these two units of measurement. One centimeter is equal to 10,000 micrometers, because there are 1,000 micrometers in a millimeter and 10 millimeters in a centimeter (1 cm = 10 mm = 10,000 µm).

The given distance is 3.4 times 10 to the negative 6th centimeters. First, converting centimeters to micrometers involves multiplying the value in centimeters by 10,000. Therefore, we can express the conversion mathematically as follows:

[

3.4 \times 10^{-6} \text{ cm} \times 10,000 \text{ µm/cm}

]

Now we perform the multiplication:

[

3.4 \times 10^{-6} \times 10,000 = 3.4 \times 10^{-6} \times 10^4

]

This simplifies to:

[

3.4 \times 10^{-2} \text{ micrometers}

]

Which is equivalent to:

[

0.034 \text{ micrometers}

]

Thus